1. (a) State two characteristics of the t-distribution that is different from the normal distribution. (b) Under what condition does the t-distribution perfectly match the normal distribution? (c) Under what condition does the t-distribution allow to test hypothesis? (d) The director of counselling in a particular university is asked if football players are doing as well academically as the other student athletes. Previous study has shown that the average GPA for the student athletes is 3.10. After an intervention to help improve the GPA of students' athletes, the director randomly samples 20 football players and find that the average GPA of the sample is 3.18 with a sample standard deviation of 0.54. Is there a significant improvement? [Take a = 0.05] 2. The transport authority in a city is implementing a fixed fare system in which a passenger may travel between two points in the city for the same fare. From the survey results, system analyses have determined an appropriate demand function, p = 2000 - 1250, where Q is the average number of riders per hour and p is the fare in Ghana cedis. (a) Determine the fare which should be charged in order to maximize hourly bus for revenue. (b) How many riders are expected per hour under this fare? (c) What is the expected